1 /* 2 * Copyright 1995-2022 The OpenSSL Project Authors. All Rights Reserved. 3 * 4 * Licensed under the OpenSSL license (the "License"). You may not use 5 * this file except in compliance with the License. You can obtain a copy 6 * in the file LICENSE in the source distribution or at 7 * https://www.openssl.org/source/license.html 8 */ 9 10 #include "internal/cryptlib.h" 11 #include "internal/constant_time.h" 12 #include "bn_local.h" 13 14 #include <stdlib.h> 15 #ifdef _WIN32 16 # include <malloc.h> 17 # ifndef alloca 18 # define alloca _alloca 19 # endif 20 #elif defined(__GNUC__) 21 # ifndef alloca 22 # define alloca(s) __builtin_alloca((s)) 23 # endif 24 #elif defined(__sun) 25 # include <alloca.h> 26 #endif 27 28 #include "rsaz_exp.h" 29 30 #undef SPARC_T4_MONT 31 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc)) 32 # include "sparc_arch.h" 33 extern unsigned int OPENSSL_sparcv9cap_P[]; 34 # define SPARC_T4_MONT 35 #endif 36 37 /* maximum precomputation table size for *variable* sliding windows */ 38 #define TABLE_SIZE 32 39 40 /* this one works - simple but works */ 41 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) 42 { 43 int i, bits, ret = 0; 44 BIGNUM *v, *rr; 45 46 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 47 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) { 48 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 49 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 50 return 0; 51 } 52 53 BN_CTX_start(ctx); 54 rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r; 55 v = BN_CTX_get(ctx); 56 if (rr == NULL || v == NULL) 57 goto err; 58 59 if (BN_copy(v, a) == NULL) 60 goto err; 61 bits = BN_num_bits(p); 62 63 if (BN_is_odd(p)) { 64 if (BN_copy(rr, a) == NULL) 65 goto err; 66 } else { 67 if (!BN_one(rr)) 68 goto err; 69 } 70 71 for (i = 1; i < bits; i++) { 72 if (!BN_sqr(v, v, ctx)) 73 goto err; 74 if (BN_is_bit_set(p, i)) { 75 if (!BN_mul(rr, rr, v, ctx)) 76 goto err; 77 } 78 } 79 if (r != rr && BN_copy(r, rr) == NULL) 80 goto err; 81 82 ret = 1; 83 err: 84 BN_CTX_end(ctx); 85 bn_check_top(r); 86 return ret; 87 } 88 89 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, 90 BN_CTX *ctx) 91 { 92 int ret; 93 94 bn_check_top(a); 95 bn_check_top(p); 96 bn_check_top(m); 97 98 /*- 99 * For even modulus m = 2^k*m_odd, it might make sense to compute 100 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery 101 * exponentiation for the odd part), using appropriate exponent 102 * reductions, and combine the results using the CRT. 103 * 104 * For now, we use Montgomery only if the modulus is odd; otherwise, 105 * exponentiation using the reciprocal-based quick remaindering 106 * algorithm is used. 107 * 108 * (Timing obtained with expspeed.c [computations a^p mod m 109 * where a, p, m are of the same length: 256, 512, 1024, 2048, 110 * 4096, 8192 bits], compared to the running time of the 111 * standard algorithm: 112 * 113 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] 114 * 55 .. 77 % [UltraSparc processor, but 115 * debug-solaris-sparcv8-gcc conf.] 116 * 117 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] 118 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] 119 * 120 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont 121 * at 2048 and more bits, but at 512 and 1024 bits, it was 122 * slower even than the standard algorithm! 123 * 124 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] 125 * should be obtained when the new Montgomery reduction code 126 * has been integrated into OpenSSL.) 127 */ 128 129 #define MONT_MUL_MOD 130 #define MONT_EXP_WORD 131 #define RECP_MUL_MOD 132 133 #ifdef MONT_MUL_MOD 134 if (BN_is_odd(m)) { 135 # ifdef MONT_EXP_WORD 136 if (a->top == 1 && !a->neg 137 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0) 138 && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0) 139 && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) { 140 BN_ULONG A = a->d[0]; 141 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL); 142 } else 143 # endif 144 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL); 145 } else 146 #endif 147 #ifdef RECP_MUL_MOD 148 { 149 ret = BN_mod_exp_recp(r, a, p, m, ctx); 150 } 151 #else 152 { 153 ret = BN_mod_exp_simple(r, a, p, m, ctx); 154 } 155 #endif 156 157 bn_check_top(r); 158 return ret; 159 } 160 161 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 162 const BIGNUM *m, BN_CTX *ctx) 163 { 164 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 165 int start = 1; 166 BIGNUM *aa; 167 /* Table of variables obtained from 'ctx' */ 168 BIGNUM *val[TABLE_SIZE]; 169 BN_RECP_CTX recp; 170 171 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 172 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 173 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 174 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 175 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 176 return 0; 177 } 178 179 bits = BN_num_bits(p); 180 if (bits == 0) { 181 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 182 if (BN_abs_is_word(m, 1)) { 183 ret = 1; 184 BN_zero(r); 185 } else { 186 ret = BN_one(r); 187 } 188 return ret; 189 } 190 191 BN_RECP_CTX_init(&recp); 192 193 BN_CTX_start(ctx); 194 aa = BN_CTX_get(ctx); 195 val[0] = BN_CTX_get(ctx); 196 if (val[0] == NULL) 197 goto err; 198 199 if (m->neg) { 200 /* ignore sign of 'm' */ 201 if (!BN_copy(aa, m)) 202 goto err; 203 aa->neg = 0; 204 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) 205 goto err; 206 } else { 207 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) 208 goto err; 209 } 210 211 if (!BN_nnmod(val[0], a, m, ctx)) 212 goto err; /* 1 */ 213 if (BN_is_zero(val[0])) { 214 BN_zero(r); 215 ret = 1; 216 goto err; 217 } 218 219 window = BN_window_bits_for_exponent_size(bits); 220 if (window > 1) { 221 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) 222 goto err; /* 2 */ 223 j = 1 << (window - 1); 224 for (i = 1; i < j; i++) { 225 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 226 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) 227 goto err; 228 } 229 } 230 231 start = 1; /* This is used to avoid multiplication etc 232 * when there is only the value '1' in the 233 * buffer. */ 234 wvalue = 0; /* The 'value' of the window */ 235 wstart = bits - 1; /* The top bit of the window */ 236 wend = 0; /* The bottom bit of the window */ 237 238 if (!BN_one(r)) 239 goto err; 240 241 for (;;) { 242 if (BN_is_bit_set(p, wstart) == 0) { 243 if (!start) 244 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 245 goto err; 246 if (wstart == 0) 247 break; 248 wstart--; 249 continue; 250 } 251 /* 252 * We now have wstart on a 'set' bit, we now need to work out how bit 253 * a window to do. To do this we need to scan forward until the last 254 * set bit before the end of the window 255 */ 256 j = wstart; 257 wvalue = 1; 258 wend = 0; 259 for (i = 1; i < window; i++) { 260 if (wstart - i < 0) 261 break; 262 if (BN_is_bit_set(p, wstart - i)) { 263 wvalue <<= (i - wend); 264 wvalue |= 1; 265 wend = i; 266 } 267 } 268 269 /* wend is the size of the current window */ 270 j = wend + 1; 271 /* add the 'bytes above' */ 272 if (!start) 273 for (i = 0; i < j; i++) { 274 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) 275 goto err; 276 } 277 278 /* wvalue will be an odd number < 2^window */ 279 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) 280 goto err; 281 282 /* move the 'window' down further */ 283 wstart -= wend + 1; 284 wvalue = 0; 285 start = 0; 286 if (wstart < 0) 287 break; 288 } 289 ret = 1; 290 err: 291 BN_CTX_end(ctx); 292 BN_RECP_CTX_free(&recp); 293 bn_check_top(r); 294 return ret; 295 } 296 297 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 298 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 299 { 300 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 301 int start = 1; 302 BIGNUM *d, *r; 303 const BIGNUM *aa; 304 /* Table of variables obtained from 'ctx' */ 305 BIGNUM *val[TABLE_SIZE]; 306 BN_MONT_CTX *mont = NULL; 307 308 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 309 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 310 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 311 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); 312 } 313 314 bn_check_top(a); 315 bn_check_top(p); 316 bn_check_top(m); 317 318 if (!BN_is_odd(m)) { 319 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS); 320 return 0; 321 } 322 bits = BN_num_bits(p); 323 if (bits == 0) { 324 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 325 if (BN_abs_is_word(m, 1)) { 326 ret = 1; 327 BN_zero(rr); 328 } else { 329 ret = BN_one(rr); 330 } 331 return ret; 332 } 333 334 BN_CTX_start(ctx); 335 d = BN_CTX_get(ctx); 336 r = BN_CTX_get(ctx); 337 val[0] = BN_CTX_get(ctx); 338 if (val[0] == NULL) 339 goto err; 340 341 /* 342 * If this is not done, things will break in the montgomery part 343 */ 344 345 if (in_mont != NULL) 346 mont = in_mont; 347 else { 348 if ((mont = BN_MONT_CTX_new()) == NULL) 349 goto err; 350 if (!BN_MONT_CTX_set(mont, m, ctx)) 351 goto err; 352 } 353 354 if (a->neg || BN_ucmp(a, m) >= 0) { 355 if (!BN_nnmod(val[0], a, m, ctx)) 356 goto err; 357 aa = val[0]; 358 } else 359 aa = a; 360 if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx)) 361 goto err; /* 1 */ 362 363 window = BN_window_bits_for_exponent_size(bits); 364 if (window > 1) { 365 if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx)) 366 goto err; /* 2 */ 367 j = 1 << (window - 1); 368 for (i = 1; i < j; i++) { 369 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 370 !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx)) 371 goto err; 372 } 373 } 374 375 start = 1; /* This is used to avoid multiplication etc 376 * when there is only the value '1' in the 377 * buffer. */ 378 wvalue = 0; /* The 'value' of the window */ 379 wstart = bits - 1; /* The top bit of the window */ 380 wend = 0; /* The bottom bit of the window */ 381 382 #if 1 /* by Shay Gueron's suggestion */ 383 j = m->top; /* borrow j */ 384 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 385 if (bn_wexpand(r, j) == NULL) 386 goto err; 387 /* 2^(top*BN_BITS2) - m */ 388 r->d[0] = (0 - m->d[0]) & BN_MASK2; 389 for (i = 1; i < j; i++) 390 r->d[i] = (~m->d[i]) & BN_MASK2; 391 r->top = j; 392 r->flags |= BN_FLG_FIXED_TOP; 393 } else 394 #endif 395 if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx)) 396 goto err; 397 for (;;) { 398 if (BN_is_bit_set(p, wstart) == 0) { 399 if (!start) { 400 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx)) 401 goto err; 402 } 403 if (wstart == 0) 404 break; 405 wstart--; 406 continue; 407 } 408 /* 409 * We now have wstart on a 'set' bit, we now need to work out how bit 410 * a window to do. To do this we need to scan forward until the last 411 * set bit before the end of the window 412 */ 413 j = wstart; 414 wvalue = 1; 415 wend = 0; 416 for (i = 1; i < window; i++) { 417 if (wstart - i < 0) 418 break; 419 if (BN_is_bit_set(p, wstart - i)) { 420 wvalue <<= (i - wend); 421 wvalue |= 1; 422 wend = i; 423 } 424 } 425 426 /* wend is the size of the current window */ 427 j = wend + 1; 428 /* add the 'bytes above' */ 429 if (!start) 430 for (i = 0; i < j; i++) { 431 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx)) 432 goto err; 433 } 434 435 /* wvalue will be an odd number < 2^window */ 436 if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx)) 437 goto err; 438 439 /* move the 'window' down further */ 440 wstart -= wend + 1; 441 wvalue = 0; 442 start = 0; 443 if (wstart < 0) 444 break; 445 } 446 /* 447 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery 448 * removes padding [if any] and makes return value suitable for public 449 * API consumer. 450 */ 451 #if defined(SPARC_T4_MONT) 452 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 453 j = mont->N.top; /* borrow j */ 454 val[0]->d[0] = 1; /* borrow val[0] */ 455 for (i = 1; i < j; i++) 456 val[0]->d[i] = 0; 457 val[0]->top = j; 458 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx)) 459 goto err; 460 } else 461 #endif 462 if (!BN_from_montgomery(rr, r, mont, ctx)) 463 goto err; 464 ret = 1; 465 err: 466 if (in_mont == NULL) 467 BN_MONT_CTX_free(mont); 468 BN_CTX_end(ctx); 469 bn_check_top(rr); 470 return ret; 471 } 472 473 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos) 474 { 475 BN_ULONG ret = 0; 476 int wordpos; 477 478 wordpos = bitpos / BN_BITS2; 479 bitpos %= BN_BITS2; 480 if (wordpos >= 0 && wordpos < a->top) { 481 ret = a->d[wordpos] & BN_MASK2; 482 if (bitpos) { 483 ret >>= bitpos; 484 if (++wordpos < a->top) 485 ret |= a->d[wordpos] << (BN_BITS2 - bitpos); 486 } 487 } 488 489 return ret & BN_MASK2; 490 } 491 492 /* 493 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific 494 * layout so that accessing any of these table values shows the same access 495 * pattern as far as cache lines are concerned. The following functions are 496 * used to transfer a BIGNUM from/to that table. 497 */ 498 499 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, 500 unsigned char *buf, int idx, 501 int window) 502 { 503 int i, j; 504 int width = 1 << window; 505 BN_ULONG *table = (BN_ULONG *)buf; 506 507 if (top > b->top) 508 top = b->top; /* this works because 'buf' is explicitly 509 * zeroed */ 510 for (i = 0, j = idx; i < top; i++, j += width) { 511 table[j] = b->d[i]; 512 } 513 514 return 1; 515 } 516 517 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, 518 unsigned char *buf, int idx, 519 int window) 520 { 521 int i, j; 522 int width = 1 << window; 523 /* 524 * We declare table 'volatile' in order to discourage compiler 525 * from reordering loads from the table. Concern is that if 526 * reordered in specific manner loads might give away the 527 * information we are trying to conceal. Some would argue that 528 * compiler can reorder them anyway, but it can as well be 529 * argued that doing so would be violation of standard... 530 */ 531 volatile BN_ULONG *table = (volatile BN_ULONG *)buf; 532 533 if (bn_wexpand(b, top) == NULL) 534 return 0; 535 536 if (window <= 3) { 537 for (i = 0; i < top; i++, table += width) { 538 BN_ULONG acc = 0; 539 540 for (j = 0; j < width; j++) { 541 acc |= table[j] & 542 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 543 } 544 545 b->d[i] = acc; 546 } 547 } else { 548 int xstride = 1 << (window - 2); 549 BN_ULONG y0, y1, y2, y3; 550 551 i = idx >> (window - 2); /* equivalent of idx / xstride */ 552 idx &= xstride - 1; /* equivalent of idx % xstride */ 553 554 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1); 555 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1); 556 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1); 557 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1); 558 559 for (i = 0; i < top; i++, table += width) { 560 BN_ULONG acc = 0; 561 562 for (j = 0; j < xstride; j++) { 563 acc |= ( (table[j + 0 * xstride] & y0) | 564 (table[j + 1 * xstride] & y1) | 565 (table[j + 2 * xstride] & y2) | 566 (table[j + 3 * xstride] & y3) ) 567 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); 568 } 569 570 b->d[i] = acc; 571 } 572 } 573 574 b->top = top; 575 b->flags |= BN_FLG_FIXED_TOP; 576 return 1; 577 } 578 579 /* 580 * Given a pointer value, compute the next address that is a cache line 581 * multiple. 582 */ 583 #define MOD_EXP_CTIME_ALIGN(x_) \ 584 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) 585 586 /* 587 * This variant of BN_mod_exp_mont() uses fixed windows and the special 588 * precomputation memory layout to limit data-dependency to a minimum to 589 * protect secret exponents (cf. the hyper-threading timing attacks pointed 590 * out by Colin Percival, 591 * http://www.daemonology.net/hyperthreading-considered-harmful/) 592 */ 593 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 594 const BIGNUM *m, BN_CTX *ctx, 595 BN_MONT_CTX *in_mont) 596 { 597 int i, bits, ret = 0, window, wvalue, wmask, window0; 598 int top; 599 BN_MONT_CTX *mont = NULL; 600 601 int numPowers; 602 unsigned char *powerbufFree = NULL; 603 int powerbufLen = 0; 604 unsigned char *powerbuf = NULL; 605 BIGNUM tmp, am; 606 #if defined(SPARC_T4_MONT) 607 unsigned int t4 = 0; 608 #endif 609 610 bn_check_top(a); 611 bn_check_top(p); 612 bn_check_top(m); 613 614 if (!BN_is_odd(m)) { 615 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS); 616 return 0; 617 } 618 619 top = m->top; 620 621 /* 622 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak 623 * whether the top bits are zero. 624 */ 625 bits = p->top * BN_BITS2; 626 if (bits == 0) { 627 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 628 if (BN_abs_is_word(m, 1)) { 629 ret = 1; 630 BN_zero(rr); 631 } else { 632 ret = BN_one(rr); 633 } 634 return ret; 635 } 636 637 BN_CTX_start(ctx); 638 639 /* 640 * Allocate a montgomery context if it was not supplied by the caller. If 641 * this is not done, things will break in the montgomery part. 642 */ 643 if (in_mont != NULL) 644 mont = in_mont; 645 else { 646 if ((mont = BN_MONT_CTX_new()) == NULL) 647 goto err; 648 if (!BN_MONT_CTX_set(mont, m, ctx)) 649 goto err; 650 } 651 652 if (a->neg || BN_ucmp(a, m) >= 0) { 653 BIGNUM *reduced = BN_CTX_get(ctx); 654 if (reduced == NULL 655 || !BN_nnmod(reduced, a, m, ctx)) { 656 goto err; 657 } 658 a = reduced; 659 } 660 661 #ifdef RSAZ_ENABLED 662 /* 663 * If the size of the operands allow it, perform the optimized 664 * RSAZ exponentiation. For further information see 665 * crypto/bn/rsaz_exp.c and accompanying assembly modules. 666 */ 667 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) 668 && rsaz_avx2_eligible()) { 669 if (NULL == bn_wexpand(rr, 16)) 670 goto err; 671 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, 672 mont->n0[0]); 673 rr->top = 16; 674 rr->neg = 0; 675 bn_correct_top(rr); 676 ret = 1; 677 goto err; 678 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) { 679 if (NULL == bn_wexpand(rr, 8)) 680 goto err; 681 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d); 682 rr->top = 8; 683 rr->neg = 0; 684 bn_correct_top(rr); 685 ret = 1; 686 goto err; 687 } 688 #endif 689 690 /* Get the window size to use with size of p. */ 691 window = BN_window_bits_for_ctime_exponent_size(bits); 692 #if defined(SPARC_T4_MONT) 693 if (window >= 5 && (top & 15) == 0 && top <= 64 && 694 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) == 695 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0])) 696 window = 5; 697 else 698 #endif 699 #if defined(OPENSSL_BN_ASM_MONT5) 700 if (window >= 5) { 701 window = 5; /* ~5% improvement for RSA2048 sign, and even 702 * for RSA4096 */ 703 /* reserve space for mont->N.d[] copy */ 704 powerbufLen += top * sizeof(mont->N.d[0]); 705 } 706 #endif 707 (void)0; 708 709 /* 710 * Allocate a buffer large enough to hold all of the pre-computed powers 711 * of am, am itself and tmp. 712 */ 713 numPowers = 1 << window; 714 powerbufLen += sizeof(m->d[0]) * (top * numPowers + 715 ((2 * top) > 716 numPowers ? (2 * top) : numPowers)); 717 #ifdef alloca 718 if (powerbufLen < 3072) 719 powerbufFree = 720 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); 721 else 722 #endif 723 if ((powerbufFree = 724 OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) 725 == NULL) 726 goto err; 727 728 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); 729 memset(powerbuf, 0, powerbufLen); 730 731 #ifdef alloca 732 if (powerbufLen < 3072) 733 powerbufFree = NULL; 734 #endif 735 736 /* lay down tmp and am right after powers table */ 737 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers); 738 am.d = tmp.d + top; 739 tmp.top = am.top = 0; 740 tmp.dmax = am.dmax = top; 741 tmp.neg = am.neg = 0; 742 tmp.flags = am.flags = BN_FLG_STATIC_DATA; 743 744 /* prepare a^0 in Montgomery domain */ 745 #if 1 /* by Shay Gueron's suggestion */ 746 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { 747 /* 2^(top*BN_BITS2) - m */ 748 tmp.d[0] = (0 - m->d[0]) & BN_MASK2; 749 for (i = 1; i < top; i++) 750 tmp.d[i] = (~m->d[i]) & BN_MASK2; 751 tmp.top = top; 752 } else 753 #endif 754 if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx)) 755 goto err; 756 757 /* prepare a^1 in Montgomery domain */ 758 if (!bn_to_mont_fixed_top(&am, a, mont, ctx)) 759 goto err; 760 761 #if defined(SPARC_T4_MONT) 762 if (t4) { 763 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np, 764 const BN_ULONG *n0, const void *table, 765 int power, int bits); 766 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np, 767 const BN_ULONG *n0, const void *table, 768 int power, int bits); 769 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np, 770 const BN_ULONG *n0, const void *table, 771 int power, int bits); 772 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np, 773 const BN_ULONG *n0, const void *table, 774 int power, int bits); 775 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np, 776 const BN_ULONG *n0, const void *table, 777 int power, int bits); 778 static const bn_pwr5_mont_f pwr5_funcs[4] = { 779 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16, 780 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 781 }; 782 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1]; 783 784 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap, 785 const void *bp, const BN_ULONG *np, 786 const BN_ULONG *n0); 787 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, 788 const BN_ULONG *np, const BN_ULONG *n0); 789 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap, 790 const void *bp, const BN_ULONG *np, 791 const BN_ULONG *n0); 792 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap, 793 const void *bp, const BN_ULONG *np, 794 const BN_ULONG *n0); 795 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap, 796 const void *bp, const BN_ULONG *np, 797 const BN_ULONG *n0); 798 static const bn_mul_mont_f mul_funcs[4] = { 799 bn_mul_mont_t4_8, bn_mul_mont_t4_16, 800 bn_mul_mont_t4_24, bn_mul_mont_t4_32 801 }; 802 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1]; 803 804 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap, 805 const void *bp, const BN_ULONG *np, 806 const BN_ULONG *n0, int num); 807 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap, 808 const void *bp, const BN_ULONG *np, 809 const BN_ULONG *n0, int num); 810 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap, 811 const void *table, const BN_ULONG *np, 812 const BN_ULONG *n0, int num, int power); 813 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num, 814 void *table, size_t power); 815 void bn_gather5_t4(BN_ULONG *out, size_t num, 816 void *table, size_t power); 817 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num); 818 819 BN_ULONG *np = mont->N.d, *n0 = mont->n0; 820 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less 821 * than 32 */ 822 823 /* 824 * BN_to_montgomery can contaminate words above .top [in 825 * BN_DEBUG[_DEBUG] build]... 826 */ 827 for (i = am.top; i < top; i++) 828 am.d[i] = 0; 829 for (i = tmp.top; i < top; i++) 830 tmp.d[i] = 0; 831 832 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0); 833 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1); 834 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) && 835 !(*mul_worker) (tmp.d, am.d, am.d, np, n0)) 836 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top); 837 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2); 838 839 for (i = 3; i < 32; i++) { 840 /* Calculate a^i = a^(i-1) * a */ 841 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) && 842 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0)) 843 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top); 844 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i); 845 } 846 847 /* switch to 64-bit domain */ 848 np = alloca(top * sizeof(BN_ULONG)); 849 top /= 2; 850 bn_flip_t4(np, mont->N.d, top); 851 852 /* 853 * The exponent may not have a whole number of fixed-size windows. 854 * To simplify the main loop, the initial window has between 1 and 855 * full-window-size bits such that what remains is always a whole 856 * number of windows 857 */ 858 window0 = (bits - 1) % 5 + 1; 859 wmask = (1 << window0) - 1; 860 bits -= window0; 861 wvalue = bn_get_bits(p, bits) & wmask; 862 bn_gather5_t4(tmp.d, top, powerbuf, wvalue); 863 864 /* 865 * Scan the exponent one window at a time starting from the most 866 * significant bits. 867 */ 868 while (bits > 0) { 869 if (bits < stride) 870 stride = bits; 871 bits -= stride; 872 wvalue = bn_get_bits(p, bits); 873 874 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 875 continue; 876 /* retry once and fall back */ 877 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) 878 continue; 879 880 bits += stride - 5; 881 wvalue >>= stride - 5; 882 wvalue &= 31; 883 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 884 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 885 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 886 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 887 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); 888 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top, 889 wvalue); 890 } 891 892 bn_flip_t4(tmp.d, tmp.d, top); 893 top *= 2; 894 /* back to 32-bit domain */ 895 tmp.top = top; 896 bn_correct_top(&tmp); 897 OPENSSL_cleanse(np, top * sizeof(BN_ULONG)); 898 } else 899 #endif 900 #if defined(OPENSSL_BN_ASM_MONT5) 901 if (window == 5 && top > 1) { 902 /* 903 * This optimization uses ideas from http://eprint.iacr.org/2011/239, 904 * specifically optimization of cache-timing attack countermeasures 905 * and pre-computation optimization. 906 */ 907 908 /* 909 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as 910 * 512-bit RSA is hardly relevant, we omit it to spare size... 911 */ 912 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, 913 const void *table, const BN_ULONG *np, 914 const BN_ULONG *n0, int num, int power); 915 void bn_scatter5(const BN_ULONG *inp, size_t num, 916 void *table, size_t power); 917 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power); 918 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, 919 const void *table, const BN_ULONG *np, 920 const BN_ULONG *n0, int num, int power); 921 int bn_get_bits5(const BN_ULONG *ap, int off); 922 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap, 923 const BN_ULONG *not_used, const BN_ULONG *np, 924 const BN_ULONG *n0, int num); 925 926 BN_ULONG *n0 = mont->n0, *np; 927 928 /* 929 * BN_to_montgomery can contaminate words above .top [in 930 * BN_DEBUG[_DEBUG] build]... 931 */ 932 for (i = am.top; i < top; i++) 933 am.d[i] = 0; 934 for (i = tmp.top; i < top; i++) 935 tmp.d[i] = 0; 936 937 /* 938 * copy mont->N.d[] to improve cache locality 939 */ 940 for (np = am.d + top, i = 0; i < top; i++) 941 np[i] = mont->N.d[i]; 942 943 bn_scatter5(tmp.d, top, powerbuf, 0); 944 bn_scatter5(am.d, am.top, powerbuf, 1); 945 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top); 946 bn_scatter5(tmp.d, top, powerbuf, 2); 947 948 # if 0 949 for (i = 3; i < 32; i++) { 950 /* Calculate a^i = a^(i-1) * a */ 951 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 952 bn_scatter5(tmp.d, top, powerbuf, i); 953 } 954 # else 955 /* same as above, but uses squaring for 1/2 of operations */ 956 for (i = 4; i < 32; i *= 2) { 957 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 958 bn_scatter5(tmp.d, top, powerbuf, i); 959 } 960 for (i = 3; i < 8; i += 2) { 961 int j; 962 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 963 bn_scatter5(tmp.d, top, powerbuf, i); 964 for (j = 2 * i; j < 32; j *= 2) { 965 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 966 bn_scatter5(tmp.d, top, powerbuf, j); 967 } 968 } 969 for (; i < 16; i += 2) { 970 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 971 bn_scatter5(tmp.d, top, powerbuf, i); 972 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 973 bn_scatter5(tmp.d, top, powerbuf, 2 * i); 974 } 975 for (; i < 32; i += 2) { 976 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); 977 bn_scatter5(tmp.d, top, powerbuf, i); 978 } 979 # endif 980 /* 981 * The exponent may not have a whole number of fixed-size windows. 982 * To simplify the main loop, the initial window has between 1 and 983 * full-window-size bits such that what remains is always a whole 984 * number of windows 985 */ 986 window0 = (bits - 1) % 5 + 1; 987 wmask = (1 << window0) - 1; 988 bits -= window0; 989 wvalue = bn_get_bits(p, bits) & wmask; 990 bn_gather5(tmp.d, top, powerbuf, wvalue); 991 992 /* 993 * Scan the exponent one window at a time starting from the most 994 * significant bits. 995 */ 996 if (top & 7) { 997 while (bits > 0) { 998 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 999 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1000 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1001 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1002 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); 1003 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, 1004 bn_get_bits5(p->d, bits -= 5)); 1005 } 1006 } else { 1007 while (bits > 0) { 1008 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, 1009 bn_get_bits5(p->d, bits -= 5)); 1010 } 1011 } 1012 1013 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top); 1014 tmp.top = top; 1015 bn_correct_top(&tmp); 1016 if (ret) { 1017 if (!BN_copy(rr, &tmp)) 1018 ret = 0; 1019 goto err; /* non-zero ret means it's not error */ 1020 } 1021 } else 1022 #endif 1023 { 1024 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window)) 1025 goto err; 1026 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window)) 1027 goto err; 1028 1029 /* 1030 * If the window size is greater than 1, then calculate 1031 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even 1032 * powers could instead be computed as (a^(i/2))^2 to use the slight 1033 * performance advantage of sqr over mul). 1034 */ 1035 if (window > 1) { 1036 if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx)) 1037 goto err; 1038 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, 1039 window)) 1040 goto err; 1041 for (i = 3; i < numPowers; i++) { 1042 /* Calculate a^i = a^(i-1) * a */ 1043 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx)) 1044 goto err; 1045 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, 1046 window)) 1047 goto err; 1048 } 1049 } 1050 1051 /* 1052 * The exponent may not have a whole number of fixed-size windows. 1053 * To simplify the main loop, the initial window has between 1 and 1054 * full-window-size bits such that what remains is always a whole 1055 * number of windows 1056 */ 1057 window0 = (bits - 1) % window + 1; 1058 wmask = (1 << window0) - 1; 1059 bits -= window0; 1060 wvalue = bn_get_bits(p, bits) & wmask; 1061 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue, 1062 window)) 1063 goto err; 1064 1065 wmask = (1 << window) - 1; 1066 /* 1067 * Scan the exponent one window at a time starting from the most 1068 * significant bits. 1069 */ 1070 while (bits > 0) { 1071 1072 /* Square the result window-size times */ 1073 for (i = 0; i < window; i++) 1074 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx)) 1075 goto err; 1076 1077 /* 1078 * Get a window's worth of bits from the exponent 1079 * This avoids calling BN_is_bit_set for each bit, which 1080 * is not only slower but also makes each bit vulnerable to 1081 * EM (and likely other) side-channel attacks like One&Done 1082 * (for details see "One&Done: A Single-Decryption EM-Based 1083 * Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam, 1084 * H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and 1085 * M. Prvulovic, in USENIX Security'18) 1086 */ 1087 bits -= window; 1088 wvalue = bn_get_bits(p, bits) & wmask; 1089 /* 1090 * Fetch the appropriate pre-computed value from the pre-buf 1091 */ 1092 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, 1093 window)) 1094 goto err; 1095 1096 /* Multiply the result into the intermediate result */ 1097 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx)) 1098 goto err; 1099 } 1100 } 1101 1102 /* 1103 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery 1104 * removes padding [if any] and makes return value suitable for public 1105 * API consumer. 1106 */ 1107 #if defined(SPARC_T4_MONT) 1108 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { 1109 am.d[0] = 1; /* borrow am */ 1110 for (i = 1; i < top; i++) 1111 am.d[i] = 0; 1112 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx)) 1113 goto err; 1114 } else 1115 #endif 1116 if (!BN_from_montgomery(rr, &tmp, mont, ctx)) 1117 goto err; 1118 ret = 1; 1119 err: 1120 if (in_mont == NULL) 1121 BN_MONT_CTX_free(mont); 1122 if (powerbuf != NULL) { 1123 OPENSSL_cleanse(powerbuf, powerbufLen); 1124 OPENSSL_free(powerbufFree); 1125 } 1126 BN_CTX_end(ctx); 1127 return ret; 1128 } 1129 1130 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, 1131 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) 1132 { 1133 BN_MONT_CTX *mont = NULL; 1134 int b, bits, ret = 0; 1135 int r_is_one; 1136 BN_ULONG w, next_w; 1137 BIGNUM *r, *t; 1138 BIGNUM *swap_tmp; 1139 #define BN_MOD_MUL_WORD(r, w, m) \ 1140 (BN_mul_word(r, (w)) && \ 1141 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ 1142 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) 1143 /* 1144 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is 1145 * probably more overhead than always using BN_mod (which uses BN_copy if 1146 * a similar test returns true). 1147 */ 1148 /* 1149 * We can use BN_mod and do not need BN_nnmod because our accumulator is 1150 * never negative (the result of BN_mod does not depend on the sign of 1151 * the modulus). 1152 */ 1153 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \ 1154 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) 1155 1156 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 1157 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 1158 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1159 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1160 return 0; 1161 } 1162 1163 bn_check_top(p); 1164 bn_check_top(m); 1165 1166 if (!BN_is_odd(m)) { 1167 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS); 1168 return 0; 1169 } 1170 if (m->top == 1) 1171 a %= m->d[0]; /* make sure that 'a' is reduced */ 1172 1173 bits = BN_num_bits(p); 1174 if (bits == 0) { 1175 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 1176 if (BN_abs_is_word(m, 1)) { 1177 ret = 1; 1178 BN_zero(rr); 1179 } else { 1180 ret = BN_one(rr); 1181 } 1182 return ret; 1183 } 1184 if (a == 0) { 1185 BN_zero(rr); 1186 ret = 1; 1187 return ret; 1188 } 1189 1190 BN_CTX_start(ctx); 1191 r = BN_CTX_get(ctx); 1192 t = BN_CTX_get(ctx); 1193 if (t == NULL) 1194 goto err; 1195 1196 if (in_mont != NULL) 1197 mont = in_mont; 1198 else { 1199 if ((mont = BN_MONT_CTX_new()) == NULL) 1200 goto err; 1201 if (!BN_MONT_CTX_set(mont, m, ctx)) 1202 goto err; 1203 } 1204 1205 r_is_one = 1; /* except for Montgomery factor */ 1206 1207 /* bits-1 >= 0 */ 1208 1209 /* The result is accumulated in the product r*w. */ 1210 w = a; /* bit 'bits-1' of 'p' is always set */ 1211 for (b = bits - 2; b >= 0; b--) { 1212 /* First, square r*w. */ 1213 next_w = w * w; 1214 if ((next_w / w) != w) { /* overflow */ 1215 if (r_is_one) { 1216 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1217 goto err; 1218 r_is_one = 0; 1219 } else { 1220 if (!BN_MOD_MUL_WORD(r, w, m)) 1221 goto err; 1222 } 1223 next_w = 1; 1224 } 1225 w = next_w; 1226 if (!r_is_one) { 1227 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 1228 goto err; 1229 } 1230 1231 /* Second, multiply r*w by 'a' if exponent bit is set. */ 1232 if (BN_is_bit_set(p, b)) { 1233 next_w = w * a; 1234 if ((next_w / a) != w) { /* overflow */ 1235 if (r_is_one) { 1236 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1237 goto err; 1238 r_is_one = 0; 1239 } else { 1240 if (!BN_MOD_MUL_WORD(r, w, m)) 1241 goto err; 1242 } 1243 next_w = a; 1244 } 1245 w = next_w; 1246 } 1247 } 1248 1249 /* Finally, set r:=r*w. */ 1250 if (w != 1) { 1251 if (r_is_one) { 1252 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) 1253 goto err; 1254 r_is_one = 0; 1255 } else { 1256 if (!BN_MOD_MUL_WORD(r, w, m)) 1257 goto err; 1258 } 1259 } 1260 1261 if (r_is_one) { /* can happen only if a == 1 */ 1262 if (!BN_one(rr)) 1263 goto err; 1264 } else { 1265 if (!BN_from_montgomery(rr, r, mont, ctx)) 1266 goto err; 1267 } 1268 ret = 1; 1269 err: 1270 if (in_mont == NULL) 1271 BN_MONT_CTX_free(mont); 1272 BN_CTX_end(ctx); 1273 bn_check_top(rr); 1274 return ret; 1275 } 1276 1277 /* The old fallback, simple version :-) */ 1278 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 1279 const BIGNUM *m, BN_CTX *ctx) 1280 { 1281 int i, j, bits, ret = 0, wstart, wend, window, wvalue; 1282 int start = 1; 1283 BIGNUM *d; 1284 /* Table of variables obtained from 'ctx' */ 1285 BIGNUM *val[TABLE_SIZE]; 1286 1287 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 1288 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 1289 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { 1290 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ 1291 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 1292 return 0; 1293 } 1294 1295 bits = BN_num_bits(p); 1296 if (bits == 0) { 1297 /* x**0 mod 1, or x**0 mod -1 is still zero. */ 1298 if (BN_abs_is_word(m, 1)) { 1299 ret = 1; 1300 BN_zero(r); 1301 } else { 1302 ret = BN_one(r); 1303 } 1304 return ret; 1305 } 1306 1307 BN_CTX_start(ctx); 1308 d = BN_CTX_get(ctx); 1309 val[0] = BN_CTX_get(ctx); 1310 if (val[0] == NULL) 1311 goto err; 1312 1313 if (!BN_nnmod(val[0], a, m, ctx)) 1314 goto err; /* 1 */ 1315 if (BN_is_zero(val[0])) { 1316 BN_zero(r); 1317 ret = 1; 1318 goto err; 1319 } 1320 1321 window = BN_window_bits_for_exponent_size(bits); 1322 if (window > 1) { 1323 if (!BN_mod_mul(d, val[0], val[0], m, ctx)) 1324 goto err; /* 2 */ 1325 j = 1 << (window - 1); 1326 for (i = 1; i < j; i++) { 1327 if (((val[i] = BN_CTX_get(ctx)) == NULL) || 1328 !BN_mod_mul(val[i], val[i - 1], d, m, ctx)) 1329 goto err; 1330 } 1331 } 1332 1333 start = 1; /* This is used to avoid multiplication etc 1334 * when there is only the value '1' in the 1335 * buffer. */ 1336 wvalue = 0; /* The 'value' of the window */ 1337 wstart = bits - 1; /* The top bit of the window */ 1338 wend = 0; /* The bottom bit of the window */ 1339 1340 if (!BN_one(r)) 1341 goto err; 1342 1343 for (;;) { 1344 if (BN_is_bit_set(p, wstart) == 0) { 1345 if (!start) 1346 if (!BN_mod_mul(r, r, r, m, ctx)) 1347 goto err; 1348 if (wstart == 0) 1349 break; 1350 wstart--; 1351 continue; 1352 } 1353 /* 1354 * We now have wstart on a 'set' bit, we now need to work out how bit 1355 * a window to do. To do this we need to scan forward until the last 1356 * set bit before the end of the window 1357 */ 1358 j = wstart; 1359 wvalue = 1; 1360 wend = 0; 1361 for (i = 1; i < window; i++) { 1362 if (wstart - i < 0) 1363 break; 1364 if (BN_is_bit_set(p, wstart - i)) { 1365 wvalue <<= (i - wend); 1366 wvalue |= 1; 1367 wend = i; 1368 } 1369 } 1370 1371 /* wend is the size of the current window */ 1372 j = wend + 1; 1373 /* add the 'bytes above' */ 1374 if (!start) 1375 for (i = 0; i < j; i++) { 1376 if (!BN_mod_mul(r, r, r, m, ctx)) 1377 goto err; 1378 } 1379 1380 /* wvalue will be an odd number < 2^window */ 1381 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx)) 1382 goto err; 1383 1384 /* move the 'window' down further */ 1385 wstart -= wend + 1; 1386 wvalue = 0; 1387 start = 0; 1388 if (wstart < 0) 1389 break; 1390 } 1391 ret = 1; 1392 err: 1393 BN_CTX_end(ctx); 1394 bn_check_top(r); 1395 return ret; 1396 } 1397